Question

Suppose that prices of Fuji apples are normally distributed. Ryan selected a simple random sample of 14 grocery stores and found that the mean price of Fuji apples at these stores was $1.84 per pound and that the standard deviation was $0.14 per pound.

Ryan plans to use this information to construct a confidence interval for ?, the mean price of a pound of Fuji apples. Have the requirements for a one-sample t?confidence interval been met?
The requirements (have/have not) been met based on these reason
a. the sample is not random.
b. the sample is random.
c. the population standard deviation is known.
d. the population is normal.
e. the sample size is too small.
f. the population is not normal.
g. the population standard deviation is not known.
h. the sample size is large enough.

Answer 1

Given that :

The prices of the Fuji apples are distributed normally.

Number of sample randomly selected = 14 grocery stores

Mean price of the Fuji apples = $ 1.84

Therefore, the requirements for a
`\text{one sample t-confidence}` interval have been made because :

• the population is normal.
• the sample is random.
• the population standard deviation is not known.